Duplicates and other problems in Media Library

Hi All.
Maybe anybody will be able to help me with this strange problem.

Situation – We have a site with a lot of blog posts (since 2010). They are important for us. As a result, we have a lot of images.
Site was updated several times since 2010 and now we have some problems with media library.
At first – search in media library stopped working. It happened half a year ago… it was not comfortable but I had no time to try to find a solution.
But today I have opened media library and found that nearly all images are duplicated.
In fact files are not duplicated – there are only posts duplicates in database – and now we have 2-4 “posts” and they are linking to one file.

So here is a question – is there a way to clean all this mess and to fix this problem?
I’m afraid that if I’ll delete duplicates from admin area, it will delete files too. How can I delete all duplicated media posts without deleting files from server?
As I understand, there are maybe some errors in some posts in DB and they are causing this problem.
Any ideas appreciated.